Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag1z)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.ag1z.01

Input Form

HypergeometricPFQ[{21/4}, {-(5/2), 23/4}, -z] == -((1463 (2 Sqrt[z] (-174881581875 + 203080878000 z - 47422851840 z^2 + 5281935360 z^3 - 378732544 z^4 + 24117248 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + (524644745625 - 1408701294000 z + 505825931520 z^2 - 74585272320 z^3 + 6323503104 z^4 - 414187520 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (524644745625 - 289459170000 z + 58864216320 z^2 - 6212358144 z^3 + 437846016 z^4 - 26214400 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(6952058880 Sqrt[2] z^(17/4)))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]